Specifically, by alibiing Satoshi, she'd made herself an accessory after the fact. If the police did manage to break Satoshi, then Shion would also be likely to go to jail. Whether they thought he was guilty or not, the Sonozakis wanted to stop that investigation.

Why would Shion go to jail for that. She only faked Satoshi alibi not killed anyone.

I think that the Mountain Hounds did it, to make the police stop searching for Satoshi.